What is the mass of an object that requires 4 nickles, 6 pennies, and 7 toothpicks to balance it

What brand toothpicks? Because they aren't all of a uniform size and weight like the coins are.

You need more specifics on those before you can arrive at an accurate answer.

And I am almost certain that there are many many many things that can make those things balance, if in the right amount. :)

So, is that the question you were given? This seems weird, if no more information is given.

Not sure you can answer that question. There are all copper pennies, steel pennies, composite pennies, silver war nickels, round toothpicks, flat toothpicks, wooden toothpicks, plastic toothpicks and the list goes on.